The Nature of Networks: A Structural Census of Degree CentralityAcross Multiple Network Sizes and Edge Densities

Benjamin Elbirt, 2007

A thesis submitted to the Faculty of the Graduate School of State University of New York at Buffalo in partial fulfillment of the requirements for the degree of MASTER OF ARTS Department of Communication

Abstract

This thesis examines the mathematical properties of networks, specifically degree centrality at the actor (node) and group (network) level. An algorithm is presented for the creation of all possible edge, node, chain and group degree structures for a given network size and edge density. The census of networks size five through fifteen are used to investigate degree distributions, degrees of freedom and effects of size and density on actor and group degree. Variability (entropy) of information based on actor and network degree centrality structure variations are provided as insight into the complexity of networks. Results indicate an underlying structural influence irrelevant of context suggesting residual data as the contextual behavior element. Power law, fat tail and low density distributions are empirically produced through non-contextual network census suggesting the current behavioral models as structural influence rather than human influence. Finally a general theory for autonomic structural influence is presented with implications for past, present and future research in the area.

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